Journal of Nonlinear Mathematical Physics

Volume 20, Issue 1, April 2013, Pages 9 - 27

Convergence to the Time Average by Stochastic Regularization

Authors
Olga Bernardi, Franco Cardin, Massimiliano Guzzo
Dipartimento di Matematica, Università degli Studi di Padova, Via Trieste, 63 - 35121 Padova, Italy
Corresponding Author
Olga Bernardi
Received 27 July 2012, Accepted 25 September 2012, Available Online 6 January 2021.
DOI
https://doi.org/10.1080/14029251.2013.792465How to use a DOI?
Keywords
Stochastic regularization techniques, approximated first integrals, Hamiltonian Perturbation Theory, Ergodic Theory
Abstract

In Ergodic Theory it is natural to consider the pointwise convergence of finite time averages of functions with respect to the flow of dynamical systems. Since the pointwise convergence is too weak for applications to Hamiltonian Perturbation Theory, requiring differentiability, we first introduce regularized averages obtained through a stochastic perturbation of an integrable Hamiltonian flow, and then we provide detailed estimates. In particular, for a special vanishing limit of the stochastic perturbation, we obtain convergence even in a Sobolev norm taking into account the derivatives.

Copyright
© 2013 The Authors. Published by Atlantis Press and Taylor & Francis
Open Access
This is an open access article distributed under the CC BY-NC 4.0 license (http://creativecommons.org/licenses/by-nc/4.0/).

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Journal
Journal of Nonlinear Mathematical Physics
Volume-Issue
20 - 1
Pages
9 - 27
Publication Date
2021/01
ISSN (Online)
1776-0852
ISSN (Print)
1402-9251
DOI
https://doi.org/10.1080/14029251.2013.792465How to use a DOI?
Copyright
© 2013 The Authors. Published by Atlantis Press and Taylor & Francis
Open Access
This is an open access article distributed under the CC BY-NC 4.0 license (http://creativecommons.org/licenses/by-nc/4.0/).

Cite this article

TY  - JOUR
AU  - Olga Bernardi
AU  - Franco Cardin
AU  - Massimiliano Guzzo
PY  - 2021
DA  - 2021/01
TI  - Convergence to the Time Average by Stochastic Regularization
JO  - Journal of Nonlinear Mathematical Physics
SP  - 9
EP  - 27
VL  - 20
IS  - 1
SN  - 1776-0852
UR  - https://doi.org/10.1080/14029251.2013.792465
DO  - https://doi.org/10.1080/14029251.2013.792465
ID  - Bernardi2021
ER  -